Luca Sabatini

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math.GR2026

On the maximal subgroups of almost simple and primitive perfect groups

Patricia Medina Capilla, Luca Sabatini

We prove that, if $G$ is a finite almost simple group and $H$ is a maximal subgroup of $G$ , then the $10$ th term of the derived series of $H$ is perfect. The same is true if $G$ is…

math.GR2026

Cayley graphs of quasirandom groups

Luca Sabatini

A finite group $G$ is $ε$ -quasirandom if all its nontrivial irreducible complex representations have degree at least $∣ G ∣^{ε}$ . Building on recent work of Golsefi…

math.GR2026

Expanding groups with large diameter

Sean Eberhard, Luca Sabatini

We study how the spectral gap and diameter of Cayley graphs depend strongly on the choice of generating set. We answer a question of Pyber and SzabÃ³ (2013) by exhibiting a sequenc…

math.GR2025

Groups that produce expander graphs

Luca Sabatini

We survey the known group properties that a sequence of finite groups or group actions needs to satisfy to admit subsets of bounded cardinality producing expander Cayley or Schreie…

math.GR2025

Quasirandom and quasisimple groups

Marco Barbieri, Luca Sabatini

Fix $ε > 0$ . We say that a finite group $G$ is $ε$ -quasirandom if every nontrivial irreducible complex representation of $G$ has degree at least $|G|^\varepsilo…

math.GR2025

On stabilizers in finite permutation groups

Luca Sabatini

Let $G$ be a permutation group on the finite set $I^c ◯$ . We prove various results about partitions of $I^c ◯$ whose stabilizers have good properties. In particular, in every solvable pe…